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r 



BWB GEOSELEIMEAIM 




A New Instrument Designed to Illustrate the Principal 
Motions and Phenomena of the Solar System. 




MANUFACTURED & FOR SALE BY 

MANUFACTURER OF 

Mathematical, Philosophical and Optical Instruments, 

£ No, 39 South 10th Street, Corner of Chestnut, 

PHILADELPHIA. 




ILLUSTRATED 



BY THE 



BY JOHN G. MOORE, M. S. 



Teacher and Lecturer in Friends' Central High School 



PHILADELPHIA, Pa, 



/ 



MANUFACTURED & FOR SALE BY 

No. 39 South 10th St., 
PHILADELPHIA, Pa. 



Entered, according to Act of Congress, in the year 1865, by 
JOHN G. MOCXRIC, 

In the Clerk's Office of the District Court of the United States, for the Eastern District of Pennsylvania, 



.&& 



M 



PBEFACE. 

In the present age, the use of demonstrative apparatus is generally 
appreciated by educators. It is conceded that truths and principles when 
illustrated make a more vivid and lasting impression on the mind. This is 
particularly the case in teaching the science of Astronomy. Tellurians, 
planetariums, etc., serve a very useful purpose in this respect, but there 
are many combined motions and phenomena of the Solar System which 
cannot be satisfactorily represented by them. A. necessity, therefore, seemed 
to exist for a more complete and comprehensive astronomical instrument. 
To supply this deficiency, the Geoselenean was invented. Since its first 
construction, however, its frequent use in the school room has suggested 
numerous improvements. As many as practicable of these have been 
added ; and in its present form, it is offered to the consideration of those 
interested in the science with the sincere hope of the inventor, that it may 
prove a valuable auxiliary in teaching. 

John G-. Moore. 

Philadelphia, November 21s*, "I860. 



— 4 — 




CONSTRUCTION. 

The Geoselenean is represented in the cut. It consists of a base A into 
which is screwed the upright post B supporting the table G upon which 
the crownwheel H is permanently attached. From the centre of H extends 
an upright pin whose lower part serves as an axis for the shaft F, and the 
upper part retains the lamp in position or answers for the sun s axis. 

Rotating upon the central pin under the pressure of the hand is the 
shaft F Sear whose outer end is an upright shaft on which the various 
horizontally moving wheels with one exception are journaled directly or 
indirectly/and on which is attached the elbow designed for the axis of the 
planet. As the said upright shaft is rotated by the gear-wheel P which 
en-a-es by means of an intermediate pinion S with the wheel M near the 
outer end of the sleeve J whose inner end carries a toothed wheel which 



— 5 — 

meshes into the crown wheel H before mentioned. It will be seen that 
the rotation of the shaft F upon its axis, rotates the sleeve J upon the 
shaft F by the engagement of the wheel L with the crown wheel H and 
the wheel M communicates revolution to the crown-wheel P through the, 
pinion S rotating the vertical shaft in such a manner that although it revolves, 
yet it retains nearly the same direction in reference to a given line in space 
The object of this -arrangement is to give the true position of the 
earth's axis and to show not only day, night, the seasons, etc ; but also 
the recession of the equinoxes and its effects. The number of the teeth 
of the wheel P is proportioned relatively to those of the wheels which ac- 
tuate it, and for instruments of moderate size the wheels L and M may 
have one-fourth as many teeth as H has, while P has one tooth less than 
H, to obtain a slow rotation of the wheel P relatively to the sun. The 
small wheel S aids in obtaining this result by reversing the direction of 
the rotation of the wheel P. 

At the outer end of the sleeve J beyond the wheel M formerly men- 
tioned are two wheels N and 0, the former of which gears into the spur- 
wheel Q, which rotates upon and independently of the inner sleeve to 
which the moon-earrier is attached. On the outer sleeve there is an ob- 
lique circular plane forming a track for the roller of the moon-carrier. 
The revolution of the wheel Q with the oblique plane preserves the moon's 
orbit in its true position in reference to the orbit of the earth. The pro- 
portion of the number of teeth in the wheels N and Q is such that Q 
makes about one-eighteenth of a revolution in the period of a year and 
thus shows the recession of the moon's nodes and regulates the phenomena 
of solar and lunar eclipses. 

The crown-wheel R is attached to the upper end of an inner sleeve and 
is revolved with it by means of the gear-wheel 0, on the end of the sleeve 
J which wheel meshes into a horizontal wheel and this again into a pinion 
on the inner sleeve. These two wheels are under the wheel Q and are 
concealed. 

The wheel R rotates about twelve times while the whole revolving sys- 
tem completes one revolution. It carries the moon around the earth and 
at the same time rotates the earth upon its-, axis by means of the engage- 
ment of the pinion on the earth's axis with the teeth of the wheel R. The 
object of the intermediate wheel beneath Q is to reverse the motion so as 
to revolve the moon and rotate the earth from west to east while the an- 
nual motion is from west to east. These motions are obtained by giving 
the pinion one-third as many teeth as and the middle wheel as many as 0. 

The table G may be inclined at pleasure being hinged to the standard 
at C, the graduated arc D indicates the angle. 

There are three elbows with corresponding inclinations to the axes of 
tne earth, Jupiter, and Venus to the planes of their respective orbits. 
These are attached by means of a screw upon the shaft in the centre of 
the wheel R, and can be changed at pleasure. The three extra moons are 
to be inserted beneath the wheel R, to illustrate the satellites of Jupiter. 
Saturn has his rings and satellites adjusted. The zenith director consists 
of an upright rod designed to be inserted into an aperture in the earth at 
the latitude of the place in which the instrument is to be used. The angle 
measurer is a rod with a graduated arc attached, to be used in connection 
with the zenith wire for determining the altitude of the sun, moon, etc. 



— 6 — 

GEOSELENEAN. 

The Geoselenean is designed to illustrate the principal motions and 
phenomena of the Solar System. The name is derived from two Greek 
words, Ge, the earth, and Selene, the moon — relating to the earth and 
moon. As the apparatus exhibits the phenomena of the other planets 
and their satellites, the name is not sufficiently comprehensive to 
indicate its full application j it expresses, however, all for which the in- 
strument was originally designed. 

GENERAL REMARKS. 

Adjustment of the Elboios. — Revolve the shaft to June 21st, as marked 
upon the zodiac ; place the elbow of the planet with the angle from the 
sun, so that the side by which it is attached, will extend in the direction 
of the shaft; and the other side which is designed for the axis of the 
planet, will be at its greatest distance from the sun. 

How the motion must be given. — The only manipulation necessary to 
give motion to the various parts of the geoselenean is the revolution of 
the main shaft. The force must be applied in the same plane in which 
the arm revolves; and, in such a manner that the motion of the shaft will 
be in a reverse direction to the hands of a watch. This simple circular 
rotation causes the combination of all the movements which represent the 
principal positions and motions of the earth and moon, or of any planet 
and its system. 



CHAPTER I. 

THE EARTH 

Motions of the Earth. — Adjust the elbow whose angle is 66$°; place 
the earth upon the pin designed for its axis; give motion to the apparatus, 
and observe that the earth not only revolves upon its own axis, but also 
that the motion is from west to east as the eastern part of any country is 
exposed to the sun before the western portion. 

The same movement which produces the diurnal motion causes simul- 
taneously the annual revolution of the earth. This is also from west to 
east as a little more than a complete revolution of the earth upon its axis, 
is necessary to bring a given meridian under the sun, and as those parts 
of the earth which are most distant from the sun, are carried by both 
motions in the same direction. It may also be shown in this connection 
that east and west are only relative terms — that the absolute direction of 
the daily motion is just opposite every twelve hours; and, of the yearly 
every six months. 

The Plane. of the Ecliptic — Inclination of the Earth's Axis. — The 
plane of the ecliptic extends through the centres of the earth and sun, 
and may be indicated as the earth revolves. The shaft in a revolution, 
describes a plane parallel to it. The earth's axis is permanently inclined 
at an angle of about 66i°, and the equinoctial at an angle of about 23£° 
to the plane of the ecliptic. 

The geoselenean is so constructed that the phenomena of the earth may 
be elucidated either when the plane is horizontal or inclined. In the for- 
mer position, the axis of the ecliptic is directed toward the zenith. The 
main facts to be explained may be exhibited while the shaft occupies this 
position, but not to the best advantage. The ecliptic plane maybe inclined 
at any angle, but there are two positions preferable to others ; first, when 



the earth's axis is directed toward the zenith; and secondly, when it ex- 
tends toward the north star. To illustrate the former, incline the shaft 
23 £° from a horizontal plane and consider the zenith as the north star 
toward which the axis then tends. An annual revolution of the earth now 
shows very clearly the oscillations of the equinoctial; that at the equinoxes 
it is directed through the centre of the sun; at the winter solstice it extends 
above, and at the summer solstice, below the sun — that it is continually 
changing yet remaining parallel to the same plane. The second inclined 
position is obtained by diverging the main arm 73J° or till the earth's 
axis is directed toward the north star. The ecliptic of the instrument 
will then be parallel to the natural ecliptic, and will well represent its di- 
rection in the heavens. The earth, too, can be brought to its exact posi- 
tion in its orbit by observing the months upon the zodiac ; when its mo- 
tions and positions, the direction of the zenith in any latitude and for any 
hour of the day will be faithfully represented. This arrangement elucidates 
the various phenomena to the best advantage as the positions as well as 
the facts are illustrated. It, however, requires more care in giving the 
motion — that it does not become too rapid. In the following explanations 
some special positions of the plane of the ecliptic will be chosen, it being 
now understood, that the one selected may be used, or any other at the 
pleasure of the operator. 

Parallelism of the earth's axis. — Direct the axis of the earth toward 
the zenith, cause the earth to complete several annual revolutions ; and 
observe that the axis continues in about the same general direction or re- 
tains a parallelism to a given line in space. When the number of revolu- 
tions exceeds ten, the fact becomes apparent that the direction of the axis 
is not absolute, but that it is slowly and gradually changing. For all illus- 
trations the recession of the equinoxes excepted, when this change be- 
comes too great, the operator should unscrew the axis and place it again 
in its first position. Ordinarily, this will not be necessary during a lesson 
or lecture as the number of revolutions which can be made without a sen- 
sible variation in the direction of the axis, is sufficiently great to illustrate 
one and even several facts. 

Altitude of the ecliptic — Zenith distance and declination of the 
sun.— The ecliptic plane appears to occupy different positions in the heavens. 
This is caused by its inclination to the equinoctial together with the an- 
nual and diurnal revolutions of the earth. The axis of the earth being 
inclined to the ecliptic plane at an angle of 6Q%°, forms with a line moved 
in this plane, angles varying from Q6$° to 113£°;' hence, the meridian al- 
titude of the ecliptic in a daily revolution of the earth, varies about 47°. 
It must be remembered, also, that a perpendicular to the earth's surface 
at latitude 40° forms with its axis an angle of 50°, which being deducted 
from the above angles will give respectively the least and greatest zenith 
distance of the sun. For convenience the following table has been arranged 
showing for latitude 40° about the zenith distance, altitude, and declina- 
tion of the sun at the time9 designated. 



TIME. ZENITH DISTANCE. 


ALTITUDE. 


DECLINATION 


March 21st, 


40° 


50° 


00 


April 21st, 


28° 


62° 


12° North 


May 20th, 


20° 


70° 


20 " 


June 21st, 


iet° 


73£° 


23|° " 


July 18th, 


19° 


71° 


21° « 


August 21st, 


28° 


62° 


12° « 


September 21st, 


40° 


50° 


00 


October 20th, 


50° 


40° 


10° South 


November 21st, 


60° 


30° 


20° « 


Dfcember 21st, 


m° 


26£° 


23£° « 


January 21st, 


60° 


30° 


20° « 


February 20 th, 


50° 


40° 


10° " 



To measure these distances ; place the zenith director on the earth at 
latitude 40°, then insert the end of the angle measurer into the small hole 
in the base of the zenith Iwire, and hold the other end so that the line 
will be in a plane parallel to the ecliptic. The graduated arc will indicate 
the zenith distance of the sun, the complement of which will be its alti- 
tude. The declination of the sun is its distance north or south of the 
equinoctial, hence when the sun is north its declination is ascertained by 
deducting the zenith distance from 40°; when south, by taking the latter 
quantity from the former. 

The plane of the ecliptic may be located by a process similar to the fol- 
lowing: bring the earth to June 21st; apply the measurer which indicates 
at midday that the sun's zenith distance is about 16£°. Cause now the 
earth to revolve slowly upon its axis, and carry the angle measurer around 
in the plane of the ecliptic ; observe that the angle increases until half a 
revolution is described when it is about 63£°, and diminished during the 
other half till it attains about its former quantity. The sun's zenith dis- 
tance at the winter solstice during midday is about 63£°, while at mid- 
night that of the ecliptic is but 16£°. In this way, the altitude of the 
ecliptic may be determined for any hour of the day, or any day of the 
year. For other latitudes, the only change necessary is the location of the 
zenith wire. A corresponding table can easily be formed. 

Zodiacal Signs. — The signs of the zodiac are represented on the table 
supporting the sun. The earth is in that sign nearest to it ; while the 
sun is in the one on the opposite side of the. sun from the earth. That is 
if the earth is in Aries, the sun is in Libra; or if the earth is in Tau- 
rus, the sun is in Scorpio, etc. The months are marked and indicate the 
time of the year when the earth and sun are in particular signs. The 
solstitial and the equinoctial points are printed upon the same plane; and 
it can, therefore, be easily determined when the earth occupies any of these 
important positions. 

Changes of the Seasons. — The changes of the seasons result from the 
inclination of the ecliptic to the equinoctial; the parallelism of the earth's 
axis; and the fact that only one half of the earth is illuminated at one 
time. To illustrate this and unequal day and night ; incline the shaft 
23£°; direct the earth's axis toward the zenith; light the lamp; darken 
the room ; and revolve the earth. A single annual revolution exhibits 
the fact that the illuminated portion of the earth changes with its position 
in its orbit. When the earth is at either equinox, it is illuminated from 
pole to pole ; when at the summer solstice its axis is inclined toward the 



— 9 — 

sun's rays exposing the north pole ; and at the winter solstice the south 
pole is. more toward the sun. 

Day and Night — Cause of their inequality. — At the vernal equinox, 
March 21st, that hemisphere of the earth is illuminated from pole to pole 
and 180° in longitude; and as the earth revolves uniformly upon its axis, 
every part of its surface is half the period of one revolution in the light 
and the other half in darkness ; therefore, over the whole globe, the days 
and nights are equal. Observe as the earth moves from the vernal equi- 
nox toward the summer solstice, that the circle of illumination changes 
both in latitude and longitude, and gradually extends beyond the north 
pole till the earth reaches the summer solstitial point, June 21st, when 
the light is limited by the Arctic circle 23 }° beyond the north pole. The 
whole of the north frigid zone is then illuminated and the days there 
exceed 24 hours in length. At the pole the day will be six months long, 
because no diurnal revolution brings this pole beyond the circle of illu- 
mination while the earth passes from the vernal to the autumnal equinox. 
In the southern hemisphere, winter reigns as the sun's rays fall most ob- 
liquely. In this region the day corresponds in length to the nigjit and 
the night, to the day of the northern hemisphere. The sun, at this point, 
is at its greatest northern declination, and its rays tall perpendicularly to 
the earth's surface at the tropic of Cancer. As the earth departs from this 
solstice toward 'the autumnal equinox, the circle of illumination so changes 
as to shorten the day and lengthen the night in the northern hemisphere, 
and produces the opposite effect in the southern. When this equinox is 
reached by the earth, the days and the nights are again equal in length. 
The revolution of the earth from this point causes the circle of illumina- 
to gradually extend beyond the south pole till the whole south frigid zone 
is enlightened, producing in that region day; while the duration of our 
day is diminished, and our nights increased. The long night then pre- 
vails in the north frigid zone varying from 24 hours to six months. As 
the earth moves forward from the winter solstice and approaches the ver- 
nal equinox, the difference between the length of the days and nights be- 
comes less and less, and entirely ceases to exist when the vernal equinox 
is reached. 

Length of the Day.^— The length of the day in any latitude may be 
easily ascertained by observing the number of degrees of longitude illu- 
minated and making a calculation similar to the following. In latitude 
40°, 200° of longitude are illuminated, April 20th. ; the length of the 
day then must be ggjj or | of 24 hours which equals 13 hours and 20 
minutes. In latitude 75°, 300° of longitude may be illuminated, hence 
360 0r 6 °f 24 hours, which equals 20 hours, the length of the day, etc. 
. Effect of a perpendicular axis. — To show the effect if the earth's axis 
were not inclined ; remove the elbow and place in its stead, the accom- 
panying one designed for Jupiter ; have the sh*ft horizontal, and observe 
that during a revolution no change of the seasons would occur, and the 
days and nights would be equal throughout the year. Showing in this 
way how different conditions affect a phenomenon, frequently renders* 
clearer those things essential to produce it. 

The Earth's orbit Elliptical. — An ellipse is a plain curve, in which the 
sum of the distances of each point from two fixed points called the foci 
is equal to a given line. Perceive that the distance between the earth 
and the sun is greater during our summer than winter, or that the earth 



— 10 — 

is in its aphelion in summer and in its perihelion in winter. By mea- 
surement, it is determined that the change of distance from one solstice 
to the other is gradual. Do not fail to notice that the portion of the orbit 
traversed by tha earth from the autumnal to the vernal equinox is shorter 
than from the vernal to the autumnal. The true figure which the earth 
describes in the geoselenean is an epicycle. The cycle is the point of at- 
tachment of the earth's axis and is equally distant from the axis about 
which the shaft revolves; it moves, therefore, in a circle; the earth in an 
annual revolution, its elbow remaining in one general direction, moves 
around this central point completing the epicycle. It may then be used 
to illustrate the cycle and the epicycle so generally resorted to in expla- 
nation of the irregularity of the motions of the planets in the Ptolemaic 
Theory and also in the Copernican prior to the discovery of the laws of 
planetary motion by Kepler. 

Sidereal & Solar Day.-k. sidereal day is the time elapsing from the transit 
of a star, to the 'transit of the same star again across the meridian. A solar 
day is the period intervening between two successive transits of the sun across 
the niSridian. As the earth revolves around the sun, the solar day is about 
4 minutes longer than the sidereal. Suppose a star in a position beyond 
the sun so that a transit of the sun and star may take place at the same 
time; revolve the earth till the star crosses the meridian which denotes a 
sidereal day; then revolve it a little farther, till the sun is on the meri- 
dian which measures the solar day. The small amount gained equals one 
whole clay in a year; and hence 366 revolutions of the earth upon its axis 
are necessary to produce 365 days. Sidereal and solar time coincide at 
the vernal equinox, and from the explanation just given, it will be inferred 
that the gain in three months is 6 hours ; in six months 12 hours, etc. 

Recession of the Equinoctial Points. — The earth is in its equinoctial 
points when the plane of the equinoctial extends through the centre of 
the sun. The parts of the earth's orbit are marked by stars. They do 
not occur, however, in the same points on the ecliptic, but are gradually 
receding by a slow movement westward completing an entire revolution 
in 25,868 years. The most direct effect of this is the revolution cf the 
pole of the earth about the pole of the ecliptic. This interesting phenom- 
enon may be thus illustrated: direct the earth* axis toward the zenith; 
observe the exact position of the vernal equinox, and revolve the earth. 
The change will scarcely be perceptible until eight or ten revolutions have 
been made. It then becomes apparent that the earth's axis is changing 
a little in direction, and that the equinoctial points are receding. In 20 
revolutions it will become very evident, in 30, the vernal equinox falls back 
to the place of the winter solstice; in 60, to the autumnal equinox when 
the axis of the earth will be inclined to its first position at an angle of 47°. 
This represents in nature 12,934 years. When 120 revolutions have been 
made, the vernal equino^has traversed the whole ecliptic and reaches 
again the starting point while the axis has made a complete revolution 
about the pole of the ecliptic, it has retained during this long period 
about the same inclination to the axis of the ecliptic. It has been directed 
to different stars, whose elevation above the horizon has been, in this lati- 
tude, the same as the north pole star, because the altitude of the north 
star is always equal to the latitude of the place of observation, The equi- 
nox occurs March 21st, and as it recedes to avoid the disarrangement of 
the months, etc., it is necessary to place the extra zodiac loosely over the 



— 11 — 

permanent one, so that it can be moved around as fast as the equinoctial 
point recedes. This will indicate, too, how the present signs of the zodiac 
differ from the constellations bearing the same names. They doubtless 
corresponded when first named. 

The cause of Recession. — The cause of the recession of the equinoxes 
is ascribed to the oblique attraction of the sun and moon upon the protu- 
berant mass of matter about the equatorial regions of the earth. To rep- 
resent this excess of matter, surround the equator of the earth with the 
plain band of paper. In accordance with the action of gravity that part 
of a body containing the greatest quantity of matter is directed towards 
the attracting body. A sphere of unequal density comes to rest with the 
heaviest portion towards the earth. As this is a very important experiment 
for the illustration of the phenomenon of recession as well as others in 
astronomy, the ball used to represent the sun has been made heavier upon 
one side and only comes to rest when free to move with that side down- 
ward. Observe when the earth is at either equinox this mass of matter 
is toward the sun and there is then no tendency to deflection as the excess 
of matter is then directly and equally attracted like the sphere at rest. 
As soon as the earth departs toward either solstice, this bulged mass be- 
comes inclined to the line of attractive force of the sun and moon. It 
reaches at the solstice the inclination 23 i° when the amount of deflective 
force is greatest. The force of attraction of the sun tends to draw this 
ring of matter to the plane of the ecliptic as the earth does the sphere 
when the heaviest part is upon one side. This would be the inevitable 
result if the force acted alone, but as it operates in conjunction with the 
rotary motion of the earth from west to east, the protuberant mass moves 
in obedience to the law of resultant motion and is twisted from east to 
west intersecting the ecliptic at each revolution ftrther westward. 

It will be readily seen as celestial longitude is reckoned eastward from 
the vernal equinox, the recession will cause an augmentation of the longi- 
tude of celestial bodies, and, therefore, it is necessary that the error should 
be rectified every few years. 

The Tropical year. — The tropical year is the time employed by the 
earth in revolving from the vernal equinox to the vernal equinox again; 
as this point is receding it does not require an entire circuit of the earth's 
orbit. The tropical year is, therefore, the amount of recession shorter 
than the sidereal year which is measured by a star. 

CHAP TEE II 

THE MOON. 

This beautiful orb is a constant attendant of the earth in its circu^i 
about the sun. It is an opaque body becoming visible to us only by re- 
flected lignt. The phenomena of the moon illustrated by the geoselenean 
appear to the best advantage when the lamp is used for the sun, and the 
experiments conducted in a dark room. It must be remembered that the 
position of the observer is supposed to be on the globe representing the 
earth, as the phenomena appear differently when viewed from other loca- 
tions. It is well for the operator to change the position of the instru- 
ment so that the relative position of the sun, earth, and moon may pre- 
sent the same appearance as they do from the earth. It is very essential 
in the illustration of the moon's altitude and eclipses that the centre of 
the moon when she is in conjunction and at her node, should be in a 



— 12 — 

straight line with the centre of the sun and earth. The adjustment is 
easily made by bending the wire carrying the moon. 

Motion of the Moon from west to east. — Observe when motion is given 
to the instrument that the moon accompanies the earth in its annual jour- 
ney; revolves about it twelve times in a year, and that her motion is from 
west to east. 

A Synodic Revolution of the Moon. — -A synodic revolution of the moon 
is the time employed by her in passing from one conjunction to the same 
conjunction again; this period is longer than the sidereal month. The 
difference is caused by the motion of the earth about the sun. 

Orbit of the Moon. — In reference to the earth the orbit of the moon i s 
an ellipse. Measure the distance of the moon from the earth at several 
points during a revolution, when it will be ascertained that she is in her 
perigee when nearest, and apogee when farthest away. The moon's motion 
combined with the earth's causes the former to produce an irregular curve 
which should, however, be concave toward the sun. 

The instrument fails to exhibit this motion correctly. The defect arises 
from the great comparative distance of the moon. She never retrogrades 
in her orbit. She only could were her distance from the earth very much 
greater. This can be shown. 

Plane of the Moon's orbit — Its inclination to the Ecliptic. — The plane 
of the moon's orbit is inclined to the ecliptic at an angle of 5£°. This is 
represented by the inclination of the circular plane which forms a track 
for the moon-roller. The plane of the orbit, however, is parallel to this, 
and passes through the centres of the earth and moon. 

Moon's Phases. — About one half of the moon's surface is illuminated at 
one time. If this enlightened hemisphere is turned towards the earth, 
the moon is full; if it is turned from the earth, the moon is invisible. 
Whatever portion of the illumined side may be toward the earth may be 
seen. As the relative positions of the earth, sun, and moon are not always 
the same, those appearances of the moon arise which are called phases. 

New Moon — First Quarter. — At the dark of the moon, the centres of 
the sun, earth, and moon are nearly in the same straight line, the moon 
being the middle body, and in conjunction. At this point, the illuminated 
surface of the moon is turned from the earth, and therefore cannot be seen. 
As soon as the moon moves a few degrees eastward of this point, a small 
portion of her illuminated hemisphere appears in a crescent form; and, 
when one fourth of a lunar revolution has been made, the moon being upon 
the meridian at sunset, about one half of her enlightened surface is ex 
posed to the earth. 

Full Moon— Third Quarter. — "From the first quarter, the moon is grad- 
ually brought into opposition when the centres of the three bodies are 
again nearly in a straight line, the earth being the middle body. The 
whole illumined hemisphere is then exposed to the earth and the moon is 
full. From this point as she moves onward, she passes through the third 
quarter, when her appearance is similar to the first, with the curved por- 
tion in the opposite direction. From this she gradually wanes and becomes 
invisible. 

Full moon at its greatest altitude in wintei New Moon at its least. — 

Having considered the altitude of the sun and ecliptic, as the moon's orbit 
is inclined only at a small angle to the earth's it will always be found near 
the plane of the ecliptic. Bring the earth to the winter solstice, and the 



— 13 — 

moon in conjunction; the sun's altitude at midday is then at its mini- 
mum. The new moon is nearly in the direction of the sun; as it can never 
depart more than 5£° from the ecliptic. Now revolve the moon to the 
point of opposition; she is full, and in crossing the meridian her altitude 
is about 47° greater than when new. This illustration as well as others 
pertaining to the altitude of the moon, is facilitated by the use of the an- 
gle measurer and zenith director; these enable the operator to determine 
with great accuracy the zenith distance, and hence the altitude of the 
moon. 

Full Moon at its least and New Moon at its greatest altitude in sum- 
mer . — Bring the earth to the summer solstice and the moon in conjunc- 
tion, she is then near the sun and at her greatest altitude. Bevolve the 
moon to opposition, she is near that part of the ecliptic in which if the 
sun were, it would have its least altitude; and, therefore, the full moon 
is low, varying from 21° to 31° above the horizon when on the meridian. 

First Quarter low, and third Quarter high at the autumnal equinox. — 
When the earth is at the autumnal equinox, and the moon in her first quar- 
ter and on the meridian, she is at that part of the ecliptic where it diver- 
ges most from the earth's axis, she is therefore low. When she passes 
around to the third quarter her altitude is about 47° greater. 

First Quarter high and third Quarter low at the vernal equinox. — A 
single lunar revolution renders this fact clear. At the equinoxes, there 
is but little difference in the altitude of the new and full moon. — It will 
be readily perceived that these variations of altitude of the moon are oc- 
casioned by the revolution of the moon; the inclination of the earth's 
axis; and the daily revolution of the earth. 

Only one side of the moon toward the earth. — The cause of the phenom- 
enon is, that the centre of gravity does not coincide with the centre of 
magnitude, and as the moon is free to change, the heaviest portion gravi- 
tates toward the earth. Use the sun again to render clear this fact. As 
a consequence, the moon revolves upon her axis in the same time she re- 
volves around the earth. In the instrument, it is evident that one side 
of the moon is constantly toward the earth. 

Moon's Librations. — The librations of the moon are of longitude and 
^atitude. Those of longitude are occasioned by the more rapid motion of 
the moon through its perigee than apogee, its revolution upon its axis be- 
ing regular. Notice that one face of the moon is toward the point of the 
moon's attachment; and, also, that the earth may be upon one side or 
the other of the centre of the wheel rotating the earth; and the moon be- 
ing viewed from these points presents different hemispheres, sometimes in- 
eluding a little more of the eastern limb, and sometimes a little more of 
the western than usual. The librations commonly called diurnal are of 
longitude and are occasioned by the distance of the observer from the 
centre of the earth. The same surface of the moon is toward the centre 
of the earth ; hence, when the moon is in the eastarn horizon more of the 
western side becomes visible; when she is in the western, more of the 
eastern can be seen. The two observations are made at a distance apart 
to correspond to 8000 miles, and the hemispheres brought to view are not 
exactly the same. 

Librations of Latitude. — The axis about which the moon rotates re- 
mains in about the same direction in space, but is not quite perpendicular 
to the plane of the moon's orbit, being inclined from the perpendicular 



— 14 — 

1£°; her orbit, too, is inclined to the ecliptic, hence, as the moon revolves 
about the earth, more of the surface about eitheF the north or the south 
pole becomes visible. The general principle may be indicated by elevating 
the moon to its highest point exhibiting a greater amount of lunar sur- 
face about its pole. 

Recession of the Moon's Nodes. — The plane of the moon's orbit being 
inclined to the ecliptic and the earth at all times being in both planes, it 
is evident that the moon in its journey around the earth is half the period 
of one revolution upon each side of the ecliptic. The points of crossing 
are called nodes. The centre of the rnoon at each revolution when at its 
node, intersects the ecliptic a little westward of its former point causing 
the phenomenon of the recession of the moon's nodes. A complete circuit 
of the ecliptic is made by the node in a period of about 18.6 years. A 
straight mark upon the middle horizontal wheel indicates the line of the 
nodes. To illustrate this recession, notice that when the moon is in the 
same direction from the earth as thi3 line that she is at her node. G-ive 
motion to the shaft till the line of the nodes extends toward the sun; 
mark the position of the earth in its orbit; revolve the earth, and observe 
that the line is directed toward the sun again before a complete annual 
revolution has been made, or in less than a year. As the moon moves on- 
ward her point of crossing the ecliptic falls backward or recedes about 
one-eighteenth each year so that when 18.2 revolutions have been com- 
pleted, the node has made an entire circuit, and is again at its starting 
point. 

The nodes are known as the ascending and the descending; the former 
occurs when the moon crosses to the northern side, and the latter, when 
she passes to the southern side of the ecliptic. 

Effect of the Recession of the Moon's nodes upon the altitude of the full 
Moon. — The recession of the moon's nodes affects and regulates to the 
amount of 101° the altitude of the full moon; that is, the full moon may 
take place 5i° north of the ecliptic, that much south of it, or any where 
between these limits. If the node months are March and September, then 
in December, the full moon occurs when she is 90° from her node, and 
at her greatest distance from the ecliptic. Presume this to be her greatest 
distance north when her altitude is about 78|°. The corresponding full 
moon the following year will take place 70° from her node, hence nearer 
the ecliptic and at a less altitude; the next year 50° from her node, 
approaching each year until December and June become the node 
months. The full moon then will have about the same altitude as the 
ecliptic or 73£°. It continues southward till the node months become 
again March and September, when her altitude is about 68|°; during the 
next nine years the change is northward, at the expiration of which time, 
her maximum altitude is again reached. The full moon in December in 
(1865) occurs north of the ecliptic, but as the node months are April and 
October, she will not attain her greatest altitude. The full moons occur- 
ring in any other month are similarly affected. The moon in any phase 
undergoes the same variation of altitude. To illustrate all these pheno- 
mena; measure the altitude of each full moon in December for a period 
corresponding to 18 years, when it will be found, that her position oscil- 
lates between two fixed points at a distance apart of 10£°. Determine 
the same thing of the moon, when she is new; at her first and third quar- 
ters; and at any season of the year. If it is desired to commence the 



— 15 — 

measurement when the full moon is at her greatest altitude, it will be ne= 
cessary to revolve the instrument till the line of the nodes becomes at right 
angles to the main shaft in December, and the moon's plane inclines to- 
ward it. 

Tides. — A band of paper with two widened portions may be placed on 
the earth oxtending around its central portion so that it may be moved at 
pleasure. Bring the earth to either equinox and the moon either to con- 
junction or opposition. Spring tides occur under these circumstances, 
and the greatest elevation of water is around the equatorial regions under 
the sun and moon. The enlarged portions represent the high water and 
they can be retained under the moon as she revolves showing that the tide 
follows the moon. One fourth of a lunar revolution shows the position 
of the earth and sun to produce neap tides. When the earth is at either 
solstice, extend the paper diagonally across its surface, to show that the 
spring tides are highest 23 £° north of the equator, and on the opposite 
side of the earth as far south of the equator ; observe then, as the earth 
revolves upon its axis that each alternate tide is higher. The paper may 
be varied to correspond to the different positions of the earth and moon 
in such a manner as to give a general idea of the tides and their positions 

. CHAPTER III. 

ECLIPSES. 

The phenomena of solar and lunar eclipses are among the most conspi- 
ciousexhibitedbytheGreoselenean. They appear to the best advantage in a 
dark room when a strong li^ht is used. The experiment is marred some- 
what by the use of so small a 'luminous body for the sun which produces 
diverging instead of converging shadows of the moon and earth. The 
disability may be partly overcome by the use of a lamp with several bur- 
ners, or of a concave mirror. 

Lunar Eclipse. — A lunar eclipse occurs when the moon is in opposi- 
tion. To illustrate an eclipse of the moon; observe that when the moon 
is full and at her node she falls into the earth's shadow in her passage 
through the point of opposition; and she is eclipsed for a longer time 
tinder these circumstances than any other because she passes through the 
central portion of the shadow, A lunar eclipse will occur when the moon 
is some degrees from her node, but it will be of shorter duration. Notice 
also, that the moon both in entering the earth's shadow and departing 
from it is partially eclipsed and that the figure of the earth's shadow is 
circular — a fact frequently adduced to illustrate the rotundity of the earth. 
The moon does not suffer an eclipse at every revolution, because her orbit 
is inclined to the ecliptic and she may in passing the point of opposition 
be either below or above the earth's shadow. 

Solar Eclipse. — An eclipse of the sun is occasioned by the interposition 
of the body of the moon intercepting a part or the whole of the sunlight. 
It can only take place at the dark of the moon and may be thus illus- 
trated: revolve the moon to conjunction, when if she is at or near her node 
she eclipses the sun. The shadow of the moon is projected distinctly upon 
the earth and passes over its equinoctial regions when the moon is exactly 
at her node, if she is some distance from it, the eclipse will be observed 
farther north or south, and the northern or southern limb of the sun will 
be obscured. As the moon's orbit is inclined, she may be when in con- 
junction sufficiently far above or below the straight line joining the cen- 



— 16 — 

tres of the earth and sun that her shadow would be cast either over or 
under the earth causing no eclipse of the sun. 

It will readily be perceived that if the orbit of the moon coincided with 
the orbit of the earth, at every revolution of the moon, there would be 
both a solar and lunar eclipse. 

All eclipses are not visible in the United States. — From the above 
illustrations, it was doubtless observed, that during a solar eclipse, the 
moon's shadow was projected upon different portions of the earth ; as, Asia, 
Africa, and South America, etc. Also during a lunar eclipse other por- 
tions of the earth than ours are turned toward the moon. Eclipses of the 
sun and moon which happen when these bodies are below our horizon are 
invisible to us. 

An Eclipse of the Sun and Moon about 15 days apart. — Upon the 
.consultation of an almanac, it is found that this year (1865) there was an 
eclipse of the moon on the 10th and one of the sun on the 25th of April. 
Although this usually happens, yet it is not universal. An eclipse of the 
sun may occur when the moon is any distance from her node not exceeding 
17°; and one of the moon when she is within 12°. While the earth 
moves through these 29° of its orbit, which requires about 29 days, 
the moon 'crosses the ecliptic twice or every 15 days; and is sufficiently 
near her node to cause both a solar and lunar eclipse. Should an eclipse 
of the sun occur, just when the moon is at her node, half a lunar revolution 
would bring the moon beyond her ecliptic limit, so that she would not 
be eclipsed. This becomes apparent by observing when the line of the 
nodes is directed nearly toward the sun, the moon being in conjunc- 
tion ; it may be revolved to opposition before the line becomes materially 
changed. 

Two Solir Eclipses about 6 Months apart. — - The two eclipses of the 
sun in 1865 are April 25th and October 19th. Mark the month that the 
line of the nodes is directed toward the sun j revolve the earth till this 
line again becomes coincident with the main shaft, which will be in a little 
less than six months. Then, when the moon is in conjunction she is suf- 
ficiently near her nodes to eclipse the sun. The time between lunar eclipses 
is also usually about six months. 

Frequency of Eclipses. — It is seen from the above that four is the usual 
number of eclipses in a year, but there may be more. Kevolve the instru- 
ment till the line of the nodes is coincident with the main shaft about the 
first of January, as it is again directed toward the sun in a little less than 
six months, the node months become June and December causing in one 
year three periods of eclipses. 

Effect of the Recession of the Moon's nodes upon Eclipses. — Bring the 
moon into conjunction and at her node; revolve the earth till the line of 
the nodes is again toward the sun which will be a period corresponding to 
346.62 days. An eclipse will not occur at this place because the moon 
will not be in conjunction; as the 346.62 days, a synodic revolution of the 
moons nodes, are not measured by 29*53 days a synodic revolution of the 
moon. There are 12 new moons in about 10 days less than a year; hence; 
the moon may be sufficiently near the node to eclipse the sun when she 
reaches her twelfth conjunction, which will cause the eclipses to take place 
about 10 days earlier each year. 

In 223 lunations which require about 18 years and 10 days, there arc 
about 19 synodic revolutions of the moon's nodes. It results from this, 



— 17 — 

that the sun, earth, and moon occupy the same relative positions every 18 
years' and 10 days. The 70 eclipses which happen in this period will take 
place in the same manner and order every cycle for ages to come. These 
eclipses will he visible from places about the same latitude but not the same 
longitude. In 1846 there were two eclipses of the sun, April 25th and Oc- 
tober 19th; in 1864 there were also two, May 5th and October 30th ; in 
1847 eclipses occurred April 15th and October 9th; in 1865, April 25th 
and October 19th. Continue the revolutions till the line of the nodes 
has made a circuit of the ecliptic which will require a period corresponding 
to 18.2 years. The cycle of eclipses is then complete and a further revolu- 
tion will repeat the eclipses in the same order. 

The Gleoselenean shows more than the real number of eclipses, especially 
of the moon, and also more of the moon than the sun, when there is a less 
number. This is occasioned by the diverging shadow of the earth. It 
will not be difficult, however, to understand why there is a greater number 
of solar than lunar eclipses. ' Two tangent lines extending from the sun 
touching the earth converge to a point. At the moon's distance from the 
earth when in opposition, these lines are about 6,000 miles apart . when 
she is in conjunction, they are about 10,000 miles apart. Eclipses happen 
when the moon is partially or entirely within these lines; one half of 
these spaces represents the distance the moon should be from the ecliptic 
to prevent an eclipse; if then she is sufficiently far from her node to be 
more than 8,000 miles and less than 5,000 miles, there may be an eclipse of 
the sun but not of the moon. Of the 70 eclipses of the Saros 41 are of 
the sun, and 29 of the moon. 

CHAPTERIV, 

THE SUN AND THE PLANETS 
The sun occupies the central portion of the apparatus and is free to re 
volve; its motion upon its axis may be shown by a hand movement, and 
the difference between its synodic and sidereal revolution illustrated. The 
sun's axis is inclined to the ecliptic at an angle of of 82f ° and toward that 
portion of it which the earth occupies in March. 

Direction of the Solar Spots. — To represent the solar spots, place upon 
the sun's surface about its equinoctial regions, small circular pieces of 
paper and revolve the sun upon its axis. During March as the sun's axis 
is inclined toward that part of the ecliptic, the spots will appear to describe 
a curve bulging downward. As the earth revolves, the curvature dimin- 
ishes until the summer solstice is reached when the spots seem to cioss in 
a straight line inclining upward. In September, they will appear again 
most curved, and as the sun's axis is most inclined from this point the 
oval part will be upward. In December, their direction is again straight 
but inclining downward. 

The Planets. — To illustrate the phenomena of the planets, it is necessary 
to place instead of the earth's elbow those corresponding to the inclination 
of the axes of the different planets ; and to use the plain balls. The main 
shaft may or may not, at the pleasure of the operator, be inclined till the 
axis of the planet will be directed toward the zenith. It may be stated, 
generally, that any phenomena which can be shown of the earth and its 
'moon, may be illustrated of all the planets and their satellites. It 
will, therefore only be essential, to indicate how the Geoselenean may be 
used to elucidate those phenomena which differ materially from the earth's, 



— 18 — 

leaving the experimenter to follow a course in other cases similar to that 
pursued in the foregoing illustrations. 

To render clearer the relative positions of the planets, an extra shaft 
has beea prepared to put temporarily upon the sun's axis. In illustration 
of the exterior planets, the earth may be placed upon this shaft; of the 
interior planets, they may sometimes occupy this position. 

Venus and Mars. — The axis of Venus is inclined to the plane of its 
orbit at an angle of 15°. Use the elbow with the obtuse angle; place the 
planet upon its axis, and give motion to the apparatus, it will be observed 
how the sun can be vertical within 15° of the poles and how the great 
obliquity produces the inequality of the seasons. As Venus has no satel- 
lite the earth's can be detached. The phases of the planet, and its elon- 
gations also become apparent, as the point of our observation is at a greater 
distance from the sun than the planet. For the axis of Mars, the earth's 
may be used, his phenomena are very similar to the earth's, he has no 
satellite. 

Jupiter. — Jupiter's axis is nearly perpendicular to his orbit; place on the 
elbow which forms nearly a right angle, and in the small apertures beneath 
the wheel giving the diurnal rotation to the planets, insert the three addi- 
tional satellites, for his fourth use the earth's. Observe in a revolution of 
Jupiter that the sun's rays fall vertically always at or near his equator ; 
and that his seasons though longer than those of the earth undergo but 
little change. His satellites are at about their relative distances, but they 
do not all revolve in the same time as the Greoselenean indicates. Three 
of them move around his equatorial regions and suffer an eclipse at every 
revolution ; this is true to nature, and is caused by their orbits being 
nearly coincident with that of the planet. The fourth moon is farther 
away and its orbit is more inclined, it may, therefore, pass the point of 
opposition without being eclipsed. These satellites except the fourth, 
eclipse the sun at every revolution and their shadows may be observed 
crossing the disk of the planet. 

Saturn. — IJor Saturn a ball has been specially prepared with rings 
encircling his equatorial regions and with seven satellites attached, the 
earth's being designed as the eighth. His axis is inclined to his orbit 63° 
rendering his seasons not much unlike those of the earth except in length. 
When Saturn is at his equinoctial points, the plane of the rings extends 
through the sun and as only the edge is then illuminated they are invisible 
to us. They also vanish when their edge is toward the earth or their 
illuminated side is, turned from the earth. At the solstitial points, the 
rings are more inclined to the direction of observation, and are most favor- 
able for being viewed. Bv a single revolution, the various positions of the 
rings become apparent. Seven of his satellites revolve in orbits nearly 
coincident with the plane of the rings, and hence are eclipsed at each rev- 
olution near the equinoxes, the eighth moves in an orbit more inclined and 
sometimes escapes. When the planet is near its solstitial point, the inclina- 
tion of the satellites, places them either above or below the planet's shadow 
bo that they are but seldom eclipsed while the planet is pursuing these 
portions of its journey. 



INDEX. 



Preface > 3 

Construction 4 

G-eoselenean— General Remarks— Earth's Motions — Plane of Ecliptic ... 6 

Parallelism of Earth's axis 7 

Altitude of Ecliptic — Zenith distance and declination of the Sun 7 

Zodiacal Signs — Changes of the Seasons 8 

Day and Night — Cause of their inequality — Length of the Day 9 

Effect of a perpendicular axis — The Earth's orbit Elliptical 9 

Sidereal and Solar Day 10 

Recession of the Equinoctial Points 10 

Cause of Recession — Tropical year — Moon 11 

Moon's Phases — Orbit — Altitude 12 

Moon's Librations of Longitude and Latitude 13 

Recession of Moon's nodes — Its effect upon the altitude of the full 

moon 14 

Tides — Lunar and Solar Eclipses 15 

Time intervening between Eclipses — Frequency of Eclipses 16 

Reoccurrence of Eclipses 16 

Direction of the Solar Spots — Planets 17 

Venus — Mars — Jupiter — Saturn . e = . . 18 



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